The practicalities of ring rolling simulation for profiled rings

Ring rolling finite element simulation for profiled rings is currently not practicable with existing Lagrangian codes and on any realistic computational platform. The main reason for this is that a large number of incremental stages are typically required for completion of a full simulation and the computational cost per increment is high. The nature of ring rolling means that the amount of deformation that takes place in a given increment is relatively small when compared with typical metal forming processes. Small errors generated over each increment can grow to give highly inaccurate predictions after not so many ring revolutions. Inaccuracies manifest themselves in volume growth, incomplete profile filling, overall dimensional inaccuracy and inaccurate force and stress level predictions. This paper describes measures that make the analysis of profiled ring rolling a more practicable proposition. A model has been developed comprising the finite element flow formulation, an arbitrary Lagrangian–Eulerian update strategy, and a novel iterative solution scheme called the successive preconditioned conjugate gradient method. The focus of the paper is on methods developed to produce accurate predictions and that ensure numerical stability for an arbitrary high number of ring revolutions. The approach adopted includes methods for volume control, circular movement stability, circular interpolation techniques for accurate transfer of state variables, contact evolution, etc. The methods are validated by comparison with earlier experimental work and previously developed models for both pure radial, and radial–axial ring rolling. In addition, some results are presented for the analysis of commercially produced railway wheels and rings.